{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q8vHMOtbxH4y"
      },
      "source": [
        "Copyright 2022 Google LLC\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "you may not use this file except in compliance with the License.\n",
        "You may obtain a copy of the License at\n",
        "\n",
        "     https://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software\n",
        "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "See the License for the specific language governing permissions and\n",
        "limitations under the License."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-mnGMLhBsSdX"
      },
      "outputs": [],
      "source": [
        "from jax import numpy as jnp\n",
        "from jax import grad\n",
        "\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "from sobolev import chebyshev\n",
        "from sobolev import sobolev\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 281
        },
        "executionInfo": {
          "elapsed": 2084,
          "status": "ok",
          "timestamp": 1647009951821,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "XlbB5XZ-sUIH",
        "outputId": "4a648604-99e4-4ab2-c399-87af28eb9d76"
      },
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAEICAYAAACnL3iHAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\nYII=\n",
            "text/plain": [
              "\u003cFigure size 600x400 with 1 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "  xx = jnp.linspace(0.1, 1, 1000)\n",
        "  yy = chebyshev.eval_chebyt(10, xx, 0.1, 1., normalization='residual')\n",
        "  \n",
        "  yy_sobolev = sobolev.eval_sobolev_chebyt(10, xx, 0.1, 1.)\n",
        "  \n",
        "  plt.title(\"P_t\")\n",
        "  plt.plot(xx, yy, lw=3, label='chebyshev')\n",
        "  plt.plot(xx, yy_sobolev, lw=3, label='sobolev')\n",
        "  plt.legend()\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 281
        },
        "executionInfo": {
          "elapsed": 31094,
          "status": "ok",
          "timestamp": 1647009983158,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "pBQ70qyjuKrJ",
        "outputId": "42f45767-3b36-4a19-b316-01b201fdb683"
      },
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEICAYAAABcVE8dAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\nAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 600x400 with 1 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "  xx = jnp.linspace(0.1, 1, 100)\n",
        "  yy = [grad(chebyshev.eval_chebyt, argnums=1)(10, x, 0.1, 1., normalization='residual') for x in xx]\n",
        "  \n",
        "  yy_sobolev = [grad(sobolev.eval_sobolev_chebyt, argnums=1)(10, x, 0.1, 1.) for x in xx]\n",
        "\n",
        "  plt.title(\"P_t'\")\n",
        "  plt.plot(xx, yy, lw=3, label='chebyshev')\n",
        "  plt.plot(xx, yy_sobolev, lw=3, label='sobolev')\n",
        "  plt.legend()\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "height": 281
        },
        "executionInfo": {
          "elapsed": 31162,
          "status": "ok",
          "timestamp": 1647010014492,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "zVMAiyxCvGQK",
        "outputId": "e1a72cff-d6de-4963-94c4-745f0d824fec"
      },
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEICAYAAABcVE8dAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90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\nYII=\n",
            "text/plain": [
              "\u003cFigure size 600x400 with 1 Axes\u003e"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "  xx = jnp.linspace(0.1, 1, 100)\n",
        "  yy = [chebyshev.eval_chebyt(10, x, 0.1, 1., normalization='residual') + grad(chebyshev.eval_chebyt, argnums=1)(10, x, 0.1, 1., normalization='residual') for x in xx]\n",
        "  \n",
        "  yy_sobolev = [sobolev.eval_sobolev_chebyt(10, x, 0.1, 1.) + grad(sobolev.eval_sobolev_chebyt, argnums=1)(10, x, 0.1, 1.) for x in xx]\n",
        "\n",
        "  plt.title(\"P_t + P_t'\")\n",
        "  plt.plot(xx, yy, lw=3, label='chebyshev')\n",
        "  plt.plot(xx, yy_sobolev, lw=3, label='sobolev')\n",
        "  plt.legend()\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OWq8BlHzx9kw"
      },
      "outputs": [],
      "source": [
        ""
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "//learning/deepmind/public/tools/ml_python:ml_notebook",
        "kind": "private"
      },
      "name": "plot sobolev.ipynb",
      "provenance": [
        {
          "file_id": "10WCAOkz0OeHJtbB7cZX9cX27cPHowEBT",
          "timestamp": 1645118379565
        }
      ]
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
